Multi-Mode Resonator Structure for Internal Resonance Suppression
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Solution Overview
Problem
Existing resonator elements face challenges in maintaining frequency accuracy due to internal resonance, which leads to steep changes in frequency characteristics that are difficult to correct, resulting in reduced accuracy.
Innovation Solution
A resonator design with a base portion and resonating arms that exhibit n inherent resonation modes, where the main resonation mode has a normalized frequency difference of at least 0.03 with other modes, and specific configurations to minimize coupling with suprious modes, including grooves on the resonating arms and specific thermal conductivity and mass density relationships, to reduce thermoelastic loss and increase Q value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the resonator element uses flexural resonation with three resonating arms, then frequency accuracy can be corrected for quadratic temperature characteristics, but internal resonance with spurious modes causes steep local changes in frequency characteristics that cannot be corrected
Solution Approach 1:
The resonator element is divided into a base portion and multiple resonating arms, where at least one resonating arm has a first resonating portion and a second resonating portion with different cross-sectional areas. This segmentation allows different portions to have different mechanical properties, enabling suppression of internal resonance while maintaining flexural resonation for frequency generation.
Solution Approach 2:
The resonating arm is designed with non-uniform cross-sectional area along its length, creating local quality variations. The first resonating portion has a different cross-sectional area than the second resonating portion, which modifies the stress distribution and vibration modes locally to suppress coupling with spurious modes while maintaining the desired flexural resonation characteristics.
2Measurement precision
If the resonator element has high Q value, then frequency accuracy improves, but internal resonance causes energy loss and reduces Q value
Solution Approach 1:
The resonator utilizes mechanical vibration in the form of flexural resonation of the resonating arms. By carefully designing the vibration mode shape through non-uniform cross-sectional areas, the resonator concentrates energy in the desired flexural mode while suppressing energy transfer to spurious modes, thereby maintaining high Q value and reducing energy loss.
Solution Approach 2:
The cross-sectional area parameter of the resonating arm is changed along its length, creating a gradient structure. This parameter variation modifies the natural frequencies and mode shapes of the resonator, separating the flexural resonation frequency from spurious modes and reducing energy loss through internal resonance.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The design effectively reduces frequency degradation due to internal resonance, enhancing frequency accuracy and achieving a high Q value, leading to a resonator with improved reliability for oscillators, electronic apparatuses, and vehicles.
Implementation Method 1
the resonator element performs resonations with n inherent resonation modes that have different resonance frequencies from one another
Implementation Method 2
specific thermal conductivity and mass density relationships, to reduce thermoelastic loss and increase Q value
Data Source
AI summary
A resonator includes: a resonator element that includes a base portion and a resonating arm; and a base. When n is one natural number of 2 or greater and j is 1 or greater and a natural number which is less than or equal to n, the resonator element performs resonations with n inherent resonation modes. In a relationship between arbitrary integers kj and resonance frequencies fj corresponding to the n inherent resonation modes, respectively, when f1 represents the resonance frequency of the main resonation of the resonator element and a normalized frequency difference Δf is defined byΔf≡(∑j=2nkjfj-k1-f1)/f1,a relationship of |Δf|≥0.03 is satisfied. The arbitrary integers kj satisfy relationships of 3≤Σj=1n|kj|≤10 and n≤Σj=1n|kj|. A ratio of an amount of a change in the resonance frequency of the main resonation, to excitation power that electrically excites the main resonation, is 20 [ppm/μW] or higher.